{
 "metadata": {
  "signature": "sha256:cc32e3184dc9ae87cb6f619a05e04c6bccb5db36eeaf70d2e9681a876e239cbc"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Filtfilt\n",
      "======================================================================\n",
      "\n",
      "This sample code demonstrates the use of the function\n",
      "scipy.signal.filtfilt, a linear filter that achieves zero phase delay by\n",
      "applying an [IIR\n",
      "filter](http://en.wikipedia.org/wiki/Infinite_impulse_response) to a\n",
      "signal twice, once forwards and once backwards. The order of the filter\n",
      "is twice the original filter order. The function also computes the\n",
      "initial filter parameters in order to provide a more stable response\n",
      "(via lfilter\\_zi).\n",
      "\n",
      "For comparison, this script also applies the same IIR filter to the\n",
      "signal using scipy.signal.lfilter; for these calculations, lfilter\\_zi\n",
      "is used to choose appropriate initial conditions for the filter. Without\n",
      "this, these plots would have long transients near 0. As it is, they have\n",
      "long transients near the initial value of the signal.\n",
      "\n",
      "Code\n",
      "----"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from numpy import sin, cos, pi, linspace\n",
      "from numpy.random import randn\n",
      "from scipy.signal import lfilter, lfilter_zi, filtfilt, butter\n",
      "\n",
      "from matplotlib.pyplot import plot, legend, show, hold, grid, figure, savefig\n",
      "\n",
      "\n",
      "# Generate a noisy signal to be filtered.\n",
      "t = linspace(-1, 1, 201)\n",
      "x = (sin(2 * pi * 0.75 * t*(1-t) + 2.1) + 0.1*sin(2 * pi * 1.25 * t + 1) +\n",
      "    0.18*cos(2 * pi * 3.85 * t))\n",
      "xn = x + randn(len(t)) * 0.08\n",
      "\n",
      "# Create an order 3 lowpass butterworth filter.\n",
      "b, a = butter(3, 0.05)\n",
      "\n",
      "# Apply the filter to xn.  Use lfilter_zi to choose the initial condition\n",
      "# of the filter.\n",
      "zi = lfilter_zi(b, a)\n",
      "z, _ = lfilter(b, a, xn, zi=zi*xn[0])\n",
      "\n",
      "# Apply the filter again, to have a result filtered at an order\n",
      "# the same as filtfilt.\n",
      "z2, _ = lfilter(b, a, z, zi=zi*z[0])\n",
      "\n",
      "# Use filtfilt to apply the filter.\n",
      "y = filtfilt(b, a, xn)\n",
      "\n",
      "\n",
      "# Make the plot.\n",
      "figure(figsize=(10,5))\n",
      "hold(True)\n",
      "plot(t, xn, 'b', linewidth=1.75, alpha=0.75)\n",
      "plot(t, z, 'r--', linewidth=1.75)\n",
      "plot(t, z2, 'r', linewidth=1.75)\n",
      "plot(t, y, 'k', linewidth=1.75)\n",
      "legend(('noisy signal',\n",
      "        'lfilter, once',\n",
      "        'lfilter, twice',\n",
      "        'filtfilt'),\n",
      "        loc='best')\n",
      "hold(False)\n",
      "grid(True)\n",
      "show()\n",
      "#savefig('plot.png', dpi=65)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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iVVElFTBGeqiGDenJvUQJSifeto36uU2ZgiCZjDQQnp7A/v3623cBQfAOOTjQ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\ng7VrzYaxOTmmMeRPf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       "text": [
        "<matplotlib.figure.Figure at 0x7f441240ca50>"
       ]
      }
     ],
     "prompt_number": 1
    }
   ],
   "metadata": {}
  }
 ]
}